Hybrid Automata as Coalgebras

Neves, Renato; Barbosa, Lu­ís Soares

doi:10.1007/978-3-319-46750-4_22

Cited by 3 publications

(5 citation statements)

References 14 publications

(24 reference statements)

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“…Due to the gravitional effect (g), it falls into the ground and then bounces back up, losing, for example, half of its kinetic energy. As the documents [NBHM16,NB16] show, such a behaviour can be described coalgebraically, with the help of the functor defined below.…”

Section: Vietoris Coalgebras At Workmentioning

confidence: 99%

“…the continuous evolutions of physical processes, such as the movement of a plane, or the temperature of a room. Document [NB16] provides the following specification for the bouncing ball described above. In order to bring non-determinism into the scene, suppose, for example, that when the ball hits the ground it loses part of its kinetic energy non-deterministically.…”

Section: Vietoris Coalgebras At Workmentioning

confidence: 99%

Section: Vietoris Coalgebras At Workmentioning

confidence: 99%

See 2 more Smart Citations

Limits in categories of Vietoris coalgebras

Hofmann¹,

Neves²,

Nora³

2018

Math. Struct. Comp. Sci.

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Motivated by the need to reason about hybrid systems, we study limits in categories of coalgebras whose underlying functor is a Vietoris polynomial one -intuitively, the topological analogue of a Kripke polynomial functor. Among other results, we prove that every Vietoris polynomial functor admits a final coalgebra if it respects certain conditions concerning separation axioms and compactness.When the functor is restricted to some of the categories induced by these conditions the resulting categories of coalgebras are even complete.As a practical application, we use these developments in the specification and analysis of nondeterministic hybrid systems, in particular to obtain suitable notions of stability, and behaviour.

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Section: Vietoris Coalgebras At Workmentioning

confidence: 99%

Section: Vietoris Coalgebras At Workmentioning

confidence: 99%

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Limits in categories of Vietoris coalgebras

Hofmann¹,

Neves²,

Nora³

2018

Math. Struct. Comp. Sci.

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“…For systems dynamics, the notion of coalgebra [20,31] provides a systematic setting, generalizing notions of transition systems that include e.g. many variants of probabilistic and stochastic transition systems [32], as well as hybrid transition systems [27]. Following the (hyper)set-based formulation of [1], a system can be described coalgebraically as a possibly infinite, mutually recursive, set of equations of the form x = F(x), where F is some operator on sets, and x some variable.…”

Section: Native Support For System Dynamicsmentioning

confidence: 99%

Counterfactual Causality from First Principles?

Gößler

Sokolsky

Stefani

2017

Electron. Proc. Theor. Comput. Sci.

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In this position paper we discuss three main shortcomings of existing approaches to counterfactual causality from the computer science perspective, and sketch lines of work to try and overcome these issues: (1) causality definitions should be driven by a set of precisely specified requirements rather than specific examples; (2) causality frameworks should support system dynamics; (3) causality analysis should have a well-understood behavior in presence of abstraction.Comment: In Proceedings CREST 2017, arXiv:1710.0277

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“…It connects probabilistic verification with coalgebraic modeling and compares expressiveness of system types by natural transformations between functors. Hybrid automata specifying both discrete and continuous behavior can also be modeled as coalgebras [24]. A coalgebraic perspective supporting a generic theory of hybrid automata with a rich palette of definitions and results is studied in [25].…”

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confidence: 99%

Fuzzy Automata as Coalgebras

Wang

Barbosa

et al. 2021

Mathematics

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The coalgebraic method is of great significance to research in process algebra, modal logic, object-oriented design and component-based software engineering. In recent years, fuzzy control has been widely used in many fields, such as handwriting recognition and the control of robots or air conditioners. It is then an interesting topic to analyze the behavior of fuzzy automata from a coalgebraic point of view. This paper models different types of fuzzy automata as coalgebras with a monad structure capturing fuzzy behavior. Based on the coalgebraic models, we can define a notion of fuzzy language and consider several versions of bisimulation for fuzzy automata. A group of combinators is defined to compose fuzzy automata of two branches: state transition and output function. A case study illustrates the coalgebraic models proposed and their composition.

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Hybrid Automata as Coalgebras

Cited by 3 publications

References 14 publications

Limits in categories of Vietoris coalgebras

Limits in categories of Vietoris coalgebras

Counterfactual Causality from First Principles?

Fuzzy Automata as Coalgebras

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